The structure of the Si(100)2 × 1: H surface

Craig, B.I.; Smith, P. V.

doi:10.1016/0039-6028(90)90144-w

Cited by 67 publications

(19 citation statements)

References 17 publications

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“…The initial oxidation, i.e., adsorption, dissociation, and migration of oxygen, on clean Si͑100͒-2ϫ1 [14][15][16][17][18] and Si͑111͒-7ϫ7 18-20 surfaces was exhaustively studied by extended Hückel, 14,19 semiempirical modified neglect of differential overlap ͑MNDO͒, 18 and first principle Hartree-Fock ͑HF͒ 15,16 and density functional theory ͑DFT͒, 17,20 using periodic slab 15,17,19,20 or cluster 14,16,18 models. The hydrogen terminated surface, in particular the Si͑100͒ surface which appears with 1ϫ1, 2ϫ1, or 3ϫ1 symmetry depending on the environment, was also subjected to the computational analyses, and the structure along with the adsorption/desorption mechanism of hydrogen on the surface were investigated by semiempirical MINDO 21,22 and PM3, 23 and ab initio HF and post-HF methods 24 and DFT. 25 In spite of its importance, however, very few theoretical studies on the oxidation of hydrogen terminated surface have been reported.…”

Section: Introductionmentioning

confidence: 99%

Quantum chemical study on the oxidation process of a hydrogen terminated Si surface

Teraishi

Takaba

Yamada

et al. 1998

The Journal of Chemical Physics

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An ab initio molecular-orbital study on hydrogen-abstraction reactions at the growing surface of hydrogenated amorphous silicon Analysis of native oxide growth process on an atomically flattened and hydrogen terminated Si (111) surface in pure water using Fourier transformed infrared reflection absorption spectroscopyThe initial oxidation process of a hydrogen terminated Si surface was investigated by molecular orbital calculations using the cluster models representing H-Si͑100͒-2ϫ1 and H-Si͑111͒-1ϫ1. Ab initio calculations using small cluster models revealed that as a Si atom is coordinated by more oxygen atoms, it increases the affinity toward another oxygen. Furthermore, the insertion of up to five oxygen atoms into Si-Si bonds of large models were traced by the semiempirical AM1 method, whose reliability was proven by comparison with ab initio results. The structural relaxation was suggested to be as important as the electronic effect on the stability of oxides, and on the HSi͑111͒-1ϫ1 surface oxidation was predicted to proceed to the second layer before its completion on the first layer to avoid a large strain which otherwise would be caused. It was also revealed that on the H-Si͑100͒-2ϫ1 surface, the growth of the oxide island and the nucleation of oxide at a distant site have almost the same probabilities. In contrast, the lateral growth of the oxide island is preferred to the formation of an isolated oxide nuclei on the H-Si͑111͒-1ϫ1 surface. These differences derive from the different Si-Si bond topology on each surface.

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Section: Introductionmentioning

confidence: 99%

Quantum chemical study on the oxidation process of a hydrogen terminated Si surface

Teraishi

Takaba

Yamada

et al. 1998

The Journal of Chemical Physics

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“…Peaks at 2π/a 0 (±1/2, ∓1/2) originate from the 2 × 1 surface reconstruction. The latter, created by symmetric dimerization of the hydrogen terminated silicon surface 57 , are found at a displacement ∆G = 2π/a 0 (∓1/2, ±1/2) relative to reciprocal lattice vectors positions. Features centered at the same coordinates were observed in the Fourier transform of the orbital probability density of donor 1 (Figure 2A and Figure A6.C) and donor 2 ( Figure A.6F), a displacement of ∆G from probability envelope features at k = 2π/a 0 (±1, ±1) and k = 0.…”

Section: Reconstruction-induced Featuresmentioning

confidence: 99%

“…The influence of displacement of surface atoms associated with the 2×1 surface reconstruction on the tight binding Hamiltonian was computed by a generalization of Harrison's scaling law 60 , assuming symmetric dimerization atomic displacements calculated elsewhere 57 . These models have been combined with the valence force field Keating model to describe atomistic strain relaxation in multi-million atom quantum dots in excellent agreement with experiments 61 .…”

Section: Theorymentioning

confidence: 99%

Spatially resolving valley quantum interference of a donor in silicon

Salfi¹,

Mol²,

Rahman³

et al. 2014

Nature Mater

105

187

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Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunctions, preventing direct experimental access to valley population, donor position, and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunneling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley perturbation-induced enhancement of spin relaxation will be negligible for depths > 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest to emerging schemes proposing to encode information directly in valley polarization. Fabrication of devices1,2 , spin readout 1 , and quantum control of spins 3,4 in silicon has been accomplished at the single-donor level. However, addressable control and coupling within qubit arrays requires local gates and control interfaces, whose atomic-scale potentials strongly influence electronic valley degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16] . While these unconventional orbital degrees of freedom play no role in conventional silicon microelectronics, they invariably arise in quantized states in indirect gap materials, and are pervasive in quantum electronics. In silicon, valley physics determines qubit relaxation rates 13,17,18 and are predicted to strongly influence two qubit gates Here, individual states of subsurface donors were measured using cryogenic scanning tunneling spectroscopy. Quantum mechanical valley interference patterns were observed in real space, associated with linear quantum superpositions of wavevectors in the six conduction band valleys of silicon. Enabled by high-accuracy empirical determination of donor depth and electric field, we perform a parameter-free comparison with atomistic theory establishing that the z-valley population is ∼ 38 ± 2% for a 2.85 ± 0.45 nm deep donor, perturbed by only ∼ 5% compared with ∼ 33.3% for a donor in bulk silicon. Consequently, donors more than 3 nm deep should not experience a significant valley-repopulation induced increase in spin-lattice relaxation. Moreover, the nearly bulklike valley interference observed will render two-qubit excha...

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“…12, 22 The impact of the surface strain due to the 2×1 reconstruction is included in the tight-binding Hamiltonian by a generalization of the Harrison's scaling law 20 , where the inter-atomic interaction energies are modified with the strained bond length d as (…”

Section: S2 Multi-million Atom Tight-binding Calculations Of Dopant mentioning

confidence: 99%

“…1(b 13,14,21 , which inherently incorporates the valley-orbit (VO) interaction in order to correctly capture the atomic fine detail for both P and As cases. As the dopants are close to the surface, the effects of dimer formation (2×1 reconstruction) 12,22 and hydrogen passivation 23 are included in the tight-binding Hamiltonian (supplementary section S2).…”

Section: Quantum Treatment Of Stm Measurementmentioning

confidence: 99%

Spatial metrology of dopants in silicon with exact lattice site precision

Usman¹,

Bocquel²,

Salfi³

et al. 2016

Nature Nanotech

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The aggressive scaling of silicon-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but more critically their position in the structure. The quantitative determination of the positions of subsurface dopant atoms is an important issue in a range of applications from channel doping in ultra-scaled transistors to quantum information processing, and hence poses a significant challenge. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pin-point the exact lattice-site location of sub-surface dopants in silicon. The technique is underpinned by the observation that STM images of sub-surface dopants typically contain many atomic-sized features in ordered patterns, which are highly sensitive to the details of the STM tip orbital and the absolute lattice-site position of the dopant atom itself. We demonstrate the technique on two types of dopant samples in silicon -the first where phosphorus dopants are placed with high precision, and a second containing randomly placed arsenic dopants. Based on the quantitative agreement between STM measurements and multi-million-atom calculations, the precise lattice site of these dopants is determined, demonstrating that the metrology works to depths of about 36 lattice planes. The ability to uniquely determine the exact positions of subsurface dopants down to depths of 5 nm will provide critical knowledge in the design and optimisation of nanoscale devices for both classical and quantum computing applications.As we approach the ultimate regime of Feynman's vision 1 of nanotechnology based on atom-by-atom fabrication 2-5 , there is a critical need to match advances in miniaturisation with atomically precise metrology. In conventional CMOS 6 and tunnelling field effect 7,8 transistors the key relationship between doping profile and performance is now dominated by the positions of just a few dopant atoms, and currently cannot be quantitatively determined. Beyond conventional nanoelectronic devices, in quantum processors based on phosphorus dopants in silicon 9 the precise locations of the individual dopants is critical to the design and operation of spin-based quantum logic gates. Previous studies on locating subsurface dopant positions in semiconductors either provide donor depths based on statistical evidence 10 , or only qualitatively locate dopants within a few nanometers region (of the order of 2.5 nm or more)11 . The key metrological challenge in all of the ultra-scaled applications is the ability to determine the position of dopant atoms in the silicon crystal substrate with lattice-site precision, which will drastically transform our understanding at the most fundamental scale leading to devices with optimised functionalities.In this work, we present an atomically precise metrology and demonstrate the pinpointing of the position of subsurface phosphorous (P) and arsenic (As) dopants in si...

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The structure of the Si(100)2 × 1: H surface

Cited by 67 publications

References 17 publications

Quantum chemical study on the oxidation process of a hydrogen terminated Si surface

Quantum chemical study on the oxidation process of a hydrogen terminated Si surface

Spatially resolving valley quantum interference of a donor in silicon

Spatial metrology of dopants in silicon with exact lattice site precision

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